"Andy is disappointed not to be competing in Japan, but on the basis of medical advice, he has decided to give his left wrist further time to recover," said a statement posted on the Scot's website.
"His injury is improving on a daily basis and Andy is very close to resuming full-training. The wrist will be assessed again this weekend."
Murray suffered the injury at the Cincinnati Masters in August and had expressed concern that he had aggravated it playing three matches for Great Britain in the Davis Cup defeat by Poland last month.
A scan ruled out the long-term damage Murray had feared but the withdrawal from the Tokyo tournament suggests the healing process has not been as quick as he had initially hoped.
Murray is still hoping to play in the Shanghai Masters, the week after the Japan Open, but it seems possible that he could skip the long trip to Asia altogether and concentrate on being fit for the Paris Masters in mid-November and ATP Tour world finals in London at the end of the month.